Hausdorff dimension of weighted singular vectors in R2

Lingmin Liao, Ronggang Shi, Omri N. Solan, Nattalie Tamam

Research output: Contribution to journalArticlepeer-review


Let w = (w1, w2) be a pair of positive real numbers with w1 + w2 = 1 and w1 ≥ w2. We show that the set of w-weighted singular vectors in R2 has Hausdorff dimension 2− 1+ 1 w 1.

Original languageEnglish
Pages (from-to)833-875
Number of pages43
JournalJournal of the European Mathematical Society
Issue number3
StatePublished - 2020


  • Diophantine approximation
  • Hausdorff dimension
  • Homogeneous dynamics
  • Weighted singular vector


Dive into the research topics of 'Hausdorff dimension of weighted singular vectors in R2'. Together they form a unique fingerprint.

Cite this